*** A make-or-break week on guns: As we’ve already previewed, this is shaping up to be a very busy month on Capitol Hill, with a shower of activity on immigration, guns, and President Obama’s budget. Yet this week in particular has become a make-or-break week when it comes to the chances of the Senate passing meaningful gun-control legislation. Here’s all the different activity, per NBC’s Kasie Hunt: Obama delivers a speech today in Hartford, CT at 5:45 pm ET after the state passed tough new gun regulations last week; Vice President Biden tomorrow holds a gun-related event at the White House; families from Newtown, CT will lobbying Capitol Hill this week after being interviewed by CBS yesterday; Senate Majority Leader Harry Reid will decide what legislation to push and how; and Senate Republicans will consider how to go forward with any filibuster. Hunt adds that there’s a glimmer of progress in negotiations over universal background checks between Sens. Joe Manchin (D-WV) and Pat Toomey (R-PA). The Washington Post has more: “Manchin and Toomey are developing a measure to require background checks for all gun purchases except sales between close family members and some hunters, which addresses concerns of some conservatives.” It’s worth pointing out that Toomey is up for re-election in increasingly blue Pennsylvania in 2016. And given that his political identity is Mr. Fiscal Conservative, he might have a little bit more freedom on a cultural issue like guns.

*** If the Manchin-Toomey negotiations break down: Hunt also reports that if the Manchin-Toomey negotiations break down, leadership aides say that Reid has considered going forward with Sen. Chuck Schumer’s background check legislation, which more than likely could be defeated by a Republican filibuster. But gun-control supporters hope that the filibuster vote would put pressure on the senators who voted not to consider the legislation. And remember, the same legislation can always be taken up a later date. For Reid, the strategy is modeled on how he dealt with “Don’t Ask, Don’t Tell.” But the gun issue may be a longer game. After all, it took two different scandals in two years -- Bill Clinton’s pardon of Marc Rich and Enron -- for Congress to pass the McCain-Feingold campaign-finance reform legislation. Political pressure and outside events are often the main drivers to get Congress to pass most legislation.

Doug Pensinger / Getty Images

President Barack Obama addresses gun control issues during a speech at the Denver Police Academy on April 3, 2013 in Denver, Colo.

*** Immigration agreement this week -- or next? In addition to the debate over guns, immigration reform remains in the spotlight. According to Schumer, the so-called Gang of 8 could reach agreement on its immigration plan by the end of the week. "We hope that we can have a bipartisan agreement among the eight of us on comprehensive immigration reform by the end of the week," he said on CBS yesterday. But fellow Gang of 8 member Lindsey Graham wasn’t on the same schedule. “We're hoping to get this thing done in the next couple of weeks,” Graham said on “Meet the Press” yesterday. Keep an eye on Marco Rubio’s body language this week as he comes back to Washington. Very important piece worth reading is this one by the Miami Herald’s Marc Caputo. Rubio may be strengthened with his conservative friends the more progressive immigration activists hound him. Then again, as Caputo points out, Rubio has walked away from big deals before when he was the Florida House Speaker.

*** Obama’s budget gets blasted from all sides: And finally this week, there’s Obama’s budget, which will be released on Wednesday -- and on the same day he dines with another group of Republican senators led by Johnny Isakson (R-GA). The early word on this budget (it essentially reflects his last offer to House Speaker John Boehner from last December, with cuts to Social Security and Medicare) has been rejected by both the right and left: Boehner opposes the president’s call for new revenues to go along with these entitlement cuts, while the left is furious about the proposed reforms to Social Security and Medicare. The question is whether this anger from the left gives Republicans a second look. Sen. Lindsey Graham appears to think so. “This is somewhat encouraging. His overall budget's not going to make it, but he has sort of made a step forward in the entitlement reform process that would allow a guy like me to begin to talk about flattening the tax code and generating more revenue,” he said on “Meet” yesterday. And with the AARP now upset with chained CPI (and promising a real electoral-style push to defeat the president’s plan), some Republicans might be asking themselves: “When is the next time we’re going to get cover from a Democratic president to touch entitlement programs?”

*** Time for Congress to start its conference committee on the budget? Yes, Obama has been late in unveiling his budget, and the criticism he’s received on this front has been deserved. But here’s our question: When is Congress going to get serious, too. It’s been weeks since both the House and Senate passed their respective budgets, but where is the talk of a conference committee? When are conferees going to be announced? Will they EVER be announced?

*** Margaret Thatcher dies: NBC has confirmed that former British PM Margaret Thatcher has died. It’s rare for a foreign to leader to be beloved by some many in the United States, but Thatcher was -- especially among conservatives. If Barry Goldwater and Ronald Reagan are the founding fathers of modern conservatism, then Margaret Thatcher is its founding mother. Thatcher also set the template for tough-as-nails female world leaders.

*** Petraeus pens op-ed: By the way, had it not been for that sex scandal late last year, this Washington Post op-ed by David Petraeus -- and co-authored by the Brookings Institution’s Michael O’Hanlon -- would be receiving A LOT of 2016 speculation. The op-ed’s title: “An American Future Filled with Promise.” But just asking, isn’t this return by Petraeus a tad too soon? After all, USA Today reported over the weekend that “FBI agents interviewed David Petraeus … at his home in Arlington on Friday… Friday's interview was part of an ongoing investigation into whether [mistress and biographer Paula] Broadwell had received classified information or whether those documents were kept in an unauthorized place, according to a federal law enforcement official.”

*** Senate Madness -- The Final: What began as a contest among history's 65-most consequential senators has been reduced to two -- Henry Clay vs. Ted Kennedy. On Friday, Clay beat Daniel Webster, and Kennedy surprisingly crushed Lyndon Johnson (thanks, we think, to the Edward M. Kennedy Institute's impressive get-out-the-vote operation). So this contest, on the same day as the NCAA basketball championship, pits Clay ("The Great Compromiser") and Kennedy ("The Last Lion"). Be sure to vote for the person you think is history's most consequential senator.